# Mechanical Properties of Twisted Carbon Nanotube Bundles with Carbon Linkers from Molecular Dynamics Simulations

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

- a
- Finite-length bundles with or without linkers made by bare CNTs for the evaluation of the intertube interaction. We also used these samples for the assessment of the ReboScr2 and DRIP potentials. For this first type of system, we performed pull-out tests. The samples were set up in 20 nm-length bundles composed of seven $(6,6)$ CNTs.
- b
- Continuous straight and twisted CNT bundles with or without linkers. In these systems, the periodicity was added to the seven $(6,6)$ CNT bundles via a periodic supercell with a longitudinal dimension of 20 nm. The model represents the physical case of a bundle composed of extra-long nanotubes.
- c
- Periodic bundles composed of finite-length CNT bundles with or without linkers for the evaluation of linkers–twisting coupling. For these bundles composed of finite-length $(6,6)$ CNTs, we shifted the outer CNT of the bundle, alternatively, up and down for 5 nm, then set up a periodic cell of 20 nm. The model represents the physical case of a long bundle composed of short nanotubes.

## 3. Results

#### 3.1. Pull-Out Test from a Nanotube Bundle

#### 3.2. Twisted Bundles Composed of Extra-Long Nanotubes under Tension

#### 3.3. Twisted Bundles Composed of Short Nanotubes under Tension

#### 3.4. Test of Novel Potentials by Means of Pull-Out Tests

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Computational model of the (6,6) CNT bundle (

**a**), showing the hexagonal symmetry of the structure; the symmetry was exploited to insert the linkers (rendered in black). The linkers are covalently bonded with the nanotubes (

**b**). Upon relaxation, they form tetravalent bonds (

**c**).

**Figure 2.**Structural models used for the simulations of the straight (

**a**) and twisted (

**b**,

**c**) $(6,6)$ CNT bundles with linkers connecting the nanotubes. The linkers are reported in black and are made of carbon atoms bonded to the nanotubes. Hydrogen atoms (in blue) saturate dangling bonds.

**Figure 3.**Top panel: pull-out stress for the central nanotube from the seven (6,6) CNT bundles with different percentages of linkers at a constant pull-out velocity of $1.0$ Å/ps. Bottom panel: cross section of the bundle with a linker percentage of $0.26$%; the color coding shows the von Mises stress distribution that decreases as the distance from the pull-out extremity increases.

**Figure 4.**Dependence of the stress–strain response on twisting and on the percentage of linkers for an infinite bundle composed of $(6,6)$ CNTs with a periodic supercell length of 20 nm. AIREBO-mod potential and a constant strain velocity equal to $1.0$ Å/ps were used.

**Figure 5.**Dependence of the tensile strength (

**top**) and of the strain at maximum stress (

**bottom**) on twisting and percentage of linkers for an infinite bundle composed of $(6,6)$ CNTs characterized by a periodic supercell of 20 nm in length. AIREBO-mod potential and a strain velocity of $1.0$ Å/ps were used.

**Figure 6.**Dependence on twisting and percentage of linkers of the stress–strain response of the bundle composed of 20 nm $(6,6)$ CNTs (

**top**). In the

**bottom**panel, a zoom of the low-strain part of the stress–strain curves reported in the top panel is shown. AIREBO-mod potential and a strain velocity of $1.0$ Å/ps were used.

**Figure 7.**Dependence on twisting and percentage of linkers of the tensile strength (

**top**) and strain at maximum stress (

**bottom**) for an infinite bundle composed of $(6,6)$ CNTs with a periodic supercell of 20 nm in length. AIREBO-mod potential and a strain velocity of $1.0$ Å/ps were used.

**Figure 8.**Dependence on twisting and percentage of linkers of Young’s modulus for an infinite bundle composed of $(6,6)$ CNTs with a periodic supercell of 20 nm in length. AIREBO-mod potential and a strain velocity of $1.0$ Å/ps were used.

**Figure 9.**Snapshot at 15% strain of the 120° twisted bundle composed of 20 nm $(6,6)$ CNTs for a percentage of linkers of $0.58$% (

**left**) and $1.53$% (

**right**). A different percentage of linkers corresponds to different failure mechanisms: the slipping of the nanotubes (

**left**) and the fracture of the nanotubes (

**right**), respectively.

**Figure 10.**Pull-out stress for the central nanotube from the seven (6,6) CNT bundles with different potentials at a constant pull-out velocity of $1.0$ Å/ps. The ReboScr2 potential overestimates the pull-out stress by a factor of two with respect to AIREBO-mod, and by 25% using the (AIREBO-mod+DRIP) interaction model.

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**MDPI and ACS Style**

Pedrielli, A.; Dapor, M.; Gkagkas, K.; Taioli, S.; Pugno, N.M.
Mechanical Properties of Twisted Carbon Nanotube Bundles with Carbon Linkers from Molecular Dynamics Simulations. *Int. J. Mol. Sci.* **2023**, *24*, 2473.
https://doi.org/10.3390/ijms24032473

**AMA Style**

Pedrielli A, Dapor M, Gkagkas K, Taioli S, Pugno NM.
Mechanical Properties of Twisted Carbon Nanotube Bundles with Carbon Linkers from Molecular Dynamics Simulations. *International Journal of Molecular Sciences*. 2023; 24(3):2473.
https://doi.org/10.3390/ijms24032473

**Chicago/Turabian Style**

Pedrielli, Andrea, Maurizio Dapor, Konstantinos Gkagkas, Simone Taioli, and Nicola Maria Pugno.
2023. "Mechanical Properties of Twisted Carbon Nanotube Bundles with Carbon Linkers from Molecular Dynamics Simulations" *International Journal of Molecular Sciences* 24, no. 3: 2473.
https://doi.org/10.3390/ijms24032473